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How to Solve Nonlinear Equations When a Third Order Method is Not Applicable

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Abstract

In this paper, we use a one-parametric family of second-order iterations to solve a nonlinear operator equation in a Banach space. A Kantorovich-type convergence theorem is proved, so that the first Fréchet derivative of the operator satisfies a Lipschitz condition. We also give an explicit error bound.

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Authors and Affiliations

  1. Department of Mathematics and Computation, University of La Rioja, C/ Luis de Ulloa s/n, ES-26004, Logroño, Spain, email

    M. A. Hernández & M. A. Salanova

Authors
  1. M. A. Hernández
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  2. M. A. Salanova
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Additional information

Supported in part by the University of La Rioja (grants: API-98/A25 and API-98/B12)and DGES (grant: PB96-0120-C03-02).

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Hernández, M.A., Salanova, M.A. How to Solve Nonlinear Equations When a Third Order Method is Not Applicable. BIT Numerical Mathematics 39, 255–269 (1999). https://doi.org/10.1023/A:1022389812813

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